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InterviewSolution
This section includes InterviewSolutions, each offering curated multiple-choice questions to sharpen your knowledge and support exam preparation. Choose a topic below to get started.
| 10751. |
If x and y are connected parametrically by the equations given in Exercises 1 to 10, without eliminating the parameter, Find (dy)/(dx). x= (sin^(3)t), y= (cos^(3)t). |
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| 10753. |
A plane passes through the points (alpha,1,0),(alpha,2,1),(-2,2,-1)and(1,1,0) for some alphainR. Then the distance of the point (1,1,1) from the plane is: |
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Answer» `(1)/(sqrt(22))` |
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| 10754. |
Let f(x)=x(x^(2)+mx+n)+2," for all" x neR and m, n in R. IfRolle's theorem holds for f(x)at x=4//3 x in[1,2], then (m+n)"equal""_______". |
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| 10755. |
Check whether the relation R defined in the set {1,2,3,4,5,6} as R = {(a,b) : b = a +1 } is reflexive , symmetric or transitive. |
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| 10756. |
Out of 13 applicants for a job, there are 5 women and 8 men. It is desired to select 2 persons for the job. The probability that atleast one of the selected persons will be a woman is |
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Answer» `10//13` |
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| 10758. |
Differentiate.sin^(-1)((2x)/(1+x^2))w.r.t.cos^(-1)((1-x^2)/(1+x^2)) |
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Answer» SOLUTION :Let `y=sin^(-1)FRAC(2x)(1+X^2)` and `z=cos ^(-1)frac(1-x^2)(1+x^2)Then `y=2 TAN ^(-1)x`and`z=2tan^(-1)x`so y=z `thereforedy/dx=1.` |
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| 10759. |
int " cosec"^(3)" x dx " |
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| 10760. |
If |{:(x,-6,-1),(2,-3x,x-3),(-3,2x,x+2):}|=0 then x = …….. |
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Answer» `-3,-2,1` |
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| 10761. |
Three houses are available in a locality. Three persons apply for the houses. Each applies for one house without consulting others. The probability that all the three apply for the same house is |
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Answer» `2//9` |
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| 10762. |
Find the condition that the curves 2x=y^(2) and 2xy = k intersect orthogonally. |
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| 10763. |
Verify the above theorem for F(x,y)=x^(2)-2y^2+2xy and x(t) = cos t, y (t) = sin t, t in[0,2pi] |
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| 10764. |
If x^(2) + ax + 1is a factor of ax^(3) + bx + c, them find the conditions. |
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Answer» `c^3=ab^3` |
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| 10765. |
Let Q be the foot the perpendicular from the origin to the plane 4x-3y+z+13=0and R be the points (-1, 1,-6)on the plane Then length QR is |
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Answer» `SQRT(14)` |
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| 10766. |
int(sqrt(1-x^2)+x^2/sqrt(1-x^2))dx |
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Answer» SOLUTION :`INT(SQRT(1-x^2)+x^2/sqrt(1-x^2))DX` =`int{(1-x^2+x^2)/sqrt(1-x^2)}dx=intdx/sqrt(1-x^2)` =`sin^-1x+C` |
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| 10768. |
Consider f(x)=sin^(-1)((x+3)/(2x+5)),g(x)=sin^(-1)((ax^(2)+b)/(x^(2)+5)). If Lim_(xto oo)(f(x)-g(x))=0 and Lim_(xto oo) (f(x)+g(x))=(pi)/(4), then find the value of (a+b^(2)). |
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Answer» Solution :`underset(xtooo)Limsin^(-1)((x+3)/(2x+5))-SIN^(-1)((ax^(2)+b)/(x^(2)+5))=0"as"xtooosin^(-1)((x+3)/(2x+5))=(PI)/(6)` `:.""underset(xtooo)Limsin^(-1)((ax^(2)+b)/(x^(2)+5))=(pi)/(6)"":.""a=(1)/(2)` Now, `underset(xtooo)Limsin^(-1)((x+3)/(2x+5))+sin^(-1)((ax^(2)+b)/(x^(2)+5))=(pi)/(4)rArr"sin"^(-1)(3)/(4)rArr+"sin"^(-1)((b)/(5))=(pi)/(4)` `sin^(-1)((b)/(5))=tan^(-1)1-"tan"^(-1)(3)/(4)rArr""sin^(-1)((b)/(5))=sin^(-1)((1)/(SQRT(50)))` `:.""b=(1)/(sqrt(2))"":.""b^(2)=(1)/(2)` `:.""a+b^(2)=1`. |
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| 10769. |
Differentiate the functions with respect to x in Exerecises 1 to 8. cos ( sin x) |
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| 10770. |
Evaluate the definite integrals int_(0)^((pi)/(2))(cos^(2)xdx)/(cos^(2)x+4sin^(2)x) |
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| 10771. |
If a die is thrown 5 times. Then find the probability that an odd number will come up exactly three times. |
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| 10773. |
A ball is dropped from a height of 48 meters and rebounds 2/3 of the distance it falls. If it continues to fall and rebound in this way, the distance the ball travels before coming to rest is |
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| 10774. |
solve abs(x^(2)-1+sinx)=abs(x^(2)-1)+abs(sinx), where x in [-2pi,2pi]. |
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| 10775. |
A unit vector coplanar with i+j+3k and i+3j+k and perpendicular to i+j+k is |
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Answer» `1/sqrt2 (j+k)` |
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| 10776. |
Write the scalar and vector components of the vector with initial point (-2, 1, 0) and terminal point (1, -5, 7). |
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Answer» VECTOR component `=3hati-6hatj+7hatk` |
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| 10777. |
For an H.P. the 3^(rd) term and 14^(th) terms are respectively 6/7 and 1/3. (i) Find the first term of H.P. (ii) Hence find the 10^(th) terms of H.P. |
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| 10778. |
If the expression ax ^(4)+bx^(3)-x ^(2)+2x+3 has the remainder 4x +3 when divided by x ^(2) + x-2, then a + 4b =….. |
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| 10779. |
(i) Slove:tan ^(-1) (x+1)+ tan ^(-1) (x-1)= tan ^(-1). (8)/(31) (ii) Slove :tan^(-1).(1)/(a-1) = tan^(-1).(1)/(x) + tan^(-1).(1)/(a^(2) - x+1) |
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| 10780. |
If alpha, beta , gamma are the roots of x^(3) + 2x^(2) - 3x + 4 = 0 then the equation whose roots beta gamma, gamma alpha, alpha betais |
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Answer» `X^(3) + 3x^(2) + 8X + 16 + 0 ` |
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| 10781. |
If a = 8,b=6 , C= 4 find tan B/2. |
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Answer» SOLUTION :If a = 8 , b = 6, c = 4 then s = (a+b+c)/2 = (8+6+4)/2 = 9 `therefore tanB/2 = sqrt((s-c)(s-a))/(s(s-b))` = `sqrt((9-4)(9-8)/9(9-6)) = sqrt(5xx1)/(9xx3) = `sqrt5/3sqrt3` |
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| 10783. |
A portion of a 24 m high tree is broken by tornado and struck the ground making an angle of 30^(@) with the ground. The height of the point where the tree is broken is equal to ___________ m |
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| 10784. |
Two fair dice are rolled. Find the probability of getting even number on the first die and odd number on the 2nd die. |
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| 10785. |
Write the converse of the following statements. (i) If a number n is even, then n^(2) is even. (ii) If you do all the exercises in the book, you get an A grade in the class. (iii) If two integers a and b are such that a gt b, then a -b is always a positive integer. |
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Answer» if a NUMBER `N^(2)` is EVEN, then n is even |
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| 10786. |
Integrate the following function : int(dx)/(sqrt((x+5)(x-1))) |
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| 10787. |
If bar(a),bar(b),bar( c ) and bar(d) are coplanar vectors then (bar(a)xx bar(b))xx(bar( c )xx bar(d))= ………….. |
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Answer» `|BAR(a)XX bar( C )|^(2)` |
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| 10788. |
The simple and weighted arithmetic mean of the first n natural numbers, the weights being the corresponding numbers is |
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Answer» `(N+1)/(2), (2n+1)/(2)` |
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| 10789. |
Express in the form ((I+i)^2)/(3-i) |
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Answer» SOLUTION : `((I+i)^2)/(3-i)=((1+i^2+2I)(3+i))/((3-i)(3+i))` `(2i(3+i))/(9-i^2)=(6I+2i^2)/(9+i)=(6i-2)/(10)` `(-2)/(10)+(6i)/(10)=- 1/5+(3I)/5` |
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| 10790. |
int (x.e^(x))/((2 + x)^(3))dx = |
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Answer» `(e^(X))/((2 + 3)^(3)) + C` |
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| 10791. |
Obtain the following integrals : int (sin^(-1)x)/((1-x^(2))^((3)/(2)))dx |
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| 10792. |
If the circle x^(2)+y^(2)=a^(2) intersects the hyperbola xy=c^(2) in four points P(x_(1),y_(1)),Q(x_(2),y_(2)),R(x_(3),y_(3)) and S(x_(4),y_(4)) then |
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Answer» `x_1 + x_2 + x_3 + x_4 =0` |
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| 10793. |
Calculate total charge present on 9.6 g of SO_(1)^(-2) ion? |
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Answer» `1.927xx10^(4)C` |
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| 10794. |
Evaluate : int " cosec"xdx |
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| 10795. |
If a**b=(ab)/3 on Q^+ then the inverse of a(a ne0) for ** is ...... |
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Answer» `3/a` |
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| 10796. |
Let PQ and RS be two parallel chords of a given circle of radius 6 cm, lying on the same side of the center. If the chords subtends angles of 72^(@)and 144^(@) at the center and the distance between the chords is d, then d^(2) is equal to |
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| 10797. |
State which of the following are positive ?Cos 271^@ |
| Answer» SOLUTION :`cos 271^@` is +ve as `271^@` LIES in 4TH QUADRANT. | |
| 10798. |
Find derivatives of the following function.(logx)^(tanx) |
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Answer» SOLUTION :`y=(LOGX)^(TANX)` `rArrlog y=tanxcdotlog(logx)` `rArr1/ydy/dx=sec^2xlog(logx)+tanxcdot1/(logx)cdot1/x` `RARR dy/dx=(logx)^(tanx){sec^2xcdotloglogx+tanx/(XLOGX)}` |
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| 10799. |
The solution of x log x (dy)/(dx) +y =1 is |
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Answer» `log x = (C)/((y-1))` |
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| 10800. |
IF Delta ABC, is an equilateral triangle, then ratio of the sides of the triangle to its ex-centre triangle is |
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Answer» `1:2` |
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